Elastic Functional Tolerance Bounds¶
Functional Tolerance Bounds using SRSF
moduleauthor:: J. Derek Tucker <jdtuck@sandia.gov>

tolerance.
bootTB
(f, time, a=0.5, p=0.99, B=500, no=5, parallel=True)[source]¶ This function computes tolerance bounds for functional data containing phase and amplitude variation using bootstrap sampling
Parameters:  f (np.ndarray) – numpy ndarray of shape (M,N) of N functions with M samples
 time (np.ndarray) – vector of size M describing the sample points
 a – confidence level of tolerance bound (default = 0.05)
 p – coverage level of tolerance bound (default = 0.99)
 B – number of bootstrap samples (default = 500)
 no – number of principal components (default = 5)
 parallel – enable parallel processing (default = T)
Return type: tuple of boxplot objects
Return amp: amplitude tolerance bounds
Rtype out_med: ampbox object
Return ph: phase tolerance bounds
Rtype out_med: phbox object
Return out_med: alignment results
Rtype out_med: fdawarp object

tolerance.
mvtol_region
(x, alpha, P, B)[source]¶ Computes tolerance factor for multivariate normal
Krishnamoorthy, K. and Mondal, S. (2006), Improved Tolerance Factors for Multivariate Normal Distributions, Communications in Statistics  Simulation and Computation, 35, 461–478.
Parameters:  x – (M,N) matrix defining N variables of M samples
 alpha – confidence level
 P – coverage level
 B – number of bootstrap samples
Return type: double
Return tol: tolerance factor

tolerance.
pcaTB
(f, time, a=0.5, p=0.99, no=5, parallel=True)[source]¶ This function computes tolerance bounds for functional data containing phase and amplitude variation using fPCA
Parameters:  f (np.ndarray) – numpy ndarray of shape (M,N) of N functions with M samples
 time (np.ndarray) – vector of size M describing the sample points
 a – confidence level of tolerance bound (default = 0.05)
 p – coverage level of tolerance bound (default = 0.99)
 no – number of principal components (default = 5)
 parallel – enable parallel processing (default = T)
Return type: tuple of boxplot objects
Return warp: alignment data from time_warping
Return pca: functional pca from jointFPCA
Return tol: tolerance factor

tolerance.
rwishart
(df, p)[source]¶ Computes a random wishart matrix
Parameters:  df – degree of freedom
 p – number of dimensions
Return type: double
Return R: matrix